Inclusive Kullback index — a macroscopic measure in ecological systems

Abstract

The expression for exergy in ecosystems given by Jørgensen and Meier includes two information-theoretical measures, that is, Kullback information ( K) and Wiener entropy ( L); the exergy is written as proportional to ( K + L). Instead of L which is scale-dependent, we introduce, as a more adequate quantity, an index M which is a scale-independent quantity. The quantity K is a measure showing the degree of departure (“distance”) of distribution of a matter among compartments in a system from that in a reference system; the quantity M is the degree of departure (“distance”) of concentration of a matter in a system from that in a reference system; and ( K + M) is the degree of departure of the state (distribution and concentration of a matter) of a system from that of a reference system. The index I = ( K + M) is a kind of extension of the concept of Kullback information K. Let I = ( K + M) be called “inclusive Kullback index”. We adopt these indices ( K, M, I) as useful macroscopic measures characterizing ecological systems. Model-calculation of these indices is made for Lake Mendota and for Lake Suwa by adopting Lake Biwa as a reference system. Hypotheses on tendency of change of these indices accompanying ecological succession are presented.